An arrangement of such a dual clutch transmission in which a freely engageable friction wheel mechanism is disposed between first and second input shafts and an output shaft, when for example a shift down is carried out the first input shaft or the second input shaft is connected to the output shaft via the friction wheel mechanism, the rotational speed of the first input shaft or the second input shaft is accelerated up to a predetermined rotational speed, and a synchronizing device is thus smoothly operated so as to reduce shift shock when shifting gears is known from Patent Document 1 below.